To get maximum current through a resistance of $2.5\,\Omega $, one can use $m$ rows of cells, each row having $n$ cells. The internal resistance of each cell is $0.5\,\Omega $. What are the values of $n$ and $m$ if the total number of cells is $45$ ?
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For maximum current,
$\mathrm{mR}=\mathrm{nr}$ ..........$(i)$
Given that $\mathrm{mn}=45$ ..........$(ii)$
Hence, $\quad \mathrm{m} \times 2.5=\mathrm{n} \times 0.5$
or $\mathrm{n}=5 \mathrm{\,m}$ .........$(iii)$
From equation $(ii)$ and $(iii),$ $5 \mathrm{m}^{2}=45$ or $\mathrm{m}=3$
$\Rightarrow \quad n=15$
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